That should work Gary. I've done something very similar before.
Can you do
var_dump($ID);
So that you are sure you get the ID correctly?
If you are getting the ID back correctly, you may try this alternative method. It works the same way, getting the View Template name but it doesn't use get_the_title.
$ID = types_render_field( "sidebar-select-view", array( "raw" => "true"));
$args = array('p' => (int)$ID, 'post_type' => 'view-template', 'limit' => 1);
$current_view = new WP_Query($args);
$current_view_title = $current_view->posts[0]->post_title;
echo do_shortcode("[wpv-post-body view_template='{$current_view_title}']");